Smallest quotients and profinite rigidity of irreducible spherical type Artin groups

Federica Gavazzi; Igor Haladjian; Luis Paris

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arXiv · 2609.25940

Smallest quotients and profinite rigidity of irreducible spherical type Artin groups

Federica Gavazzi·Igor Haladjian·Luis Paris

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Abstract

We prove that irreducible spherical type Artin groups are profinitely rigid within the class of all spherical type Artin groups. As part of the proof, building on ideas of Kolay for the $n$-strand braid group, we compute the smallest non-abelian quotient of every spherical type Artin group. In particular, given an irreducible spherical type Artin group, its smallest non-abelian quotient is always that of the corresponding Coxeter group, except for dihedral Artin groups of weight divisible by $4$, which all have $\mathfrak S_3$ as a non-abelian quotient. Parts of the proof also rely on the computation of the cohomological dimension of the profinite completion of certain Artin groups.

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Federica Gavazzi, Igor Haladjian, Luis Paris. 2026-09-22. Smallest quotients and profinite rigidity of irreducible spherical type Artin groups. https://arxiv.org/abs/2609.25940

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